I define S as empty set:

S = {}

Why the Cartesian product S x A (A is not empty set) not defined?

Is

(2) S x S x A

(3) A x S

(4) S x A x S

defined?

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- Jun 11th 2018, 01:54 AMpolicerempty set
I define S as empty set:

S = {}

Why the Cartesian product S x A (A is not empty set) not defined?

Is

(2) S x S x A

(3) A x S

(4) S x A x S

defined? - Jun 11th 2018, 04:42 AMSlipEternalRe: empty set
It may not be defined in your book, but other books define it. Here is how one might define the Cartesian product with the empty set:

Given sets $A,B$, we define $A\times B = \{(a,b)|a\in A, b\in B\}$. If $A=\emptyset$, then there are no candidate choices for $a\in A$, so there are no ordered pairs in $A\times B$, making it the empty set. Similarly if $B=\emptyset$.